The constants in each case were evaluated by successive approximations. The corresponding pairs of individual isotherms, however, are quite different from each other (Fig. 5) and also differ from those obtained by a more direct method described below (cf. Fig. 8). This emphasizes the relative ease of fitting a simple curve with an equation containing four adjustable constants. Such an equation may have no signi­ ficance in terms of a model for the physical system being considered. In the present case, pressure terms were replaced by concentration terms in the Langmuir equation.

G. x ^ 0-01) In such cases, even if n\ is considerable, the term n\ x can be neglected, to a first approximation. Similarly, the term n\{\ —x) approximates to n\ because (1— x) is nearly equal to one. This situation often applies to solutions of solids in liquids because the solubility limit is low in terms of mole fractions. If the solid is very soluble in the liquid, however, the approximation is a bad one. Although n\ can be obtained in this way, the corresponding value of n\ is not obtained, and for this another method is needed.

The composite isotherm is sometimes expressed in terms of (χΙ — Χχ), where x* is the mole fraction of component 1 in the adsorbed layer. This form emphasizes the preferential adsorption of one component. It can readily be shown that *-*i=A-°-. 15 3. ADSORPTION AT THE LIQUID-SOLID INTERFACE 29 where ns is the total number of molecules in the adsorbed layer on unit weight of solid. Hence n\x\ — x j = n\(l — Xi) — ns2Xi. 6) m where w0 is the initial weight of liquid brought in contact with a weight m of adsorbent; the equilibrium weight fraction of the solution is c, and wf and w'J are the weights of the two components, respectively, adsorbed by unit weight of adsorbent.